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A072829
Greatest m such that Product_{k=1..n-1} (1 - k/m) <= 1/2.
2
2, 5, 9, 16, 23, 32, 42, 54, 68, 82, 99, 116, 135, 156, 178, 201, 226, 252, 280, 309, 340, 372, 406, 441, 477, 515, 554, 595, 637, 681, 726, 772, 820, 869, 920, 973, 1026, 1081, 1138, 1196, 1256, 1316, 1379, 1443, 1508, 1575, 1643, 1712, 1783, 1856, 1930, 2005
OFFSET
2,1
COMMENTS
Among n randomly selected dates over an interval of m days (or less), the odds are even (or better than even) for two or more of them to coincide.
FORMULA
Corresponds to the ultimate occurrence of n in A033810. For large n, m has magnitude n^2 / 2 * log(2).
EXAMPLE
Thus a(7)=32 for instance implies that among 7 persons bearing the same astrological sign(extending over 30 days or so) the odds are trifle better than even for at least two of them further sharing a common birthday.
MATHEMATICA
f[n_] := (k = 1; While[ Product[1 - i/k, {i, 1, (n - 1)}] <= 1/2, k++ ]; Return[k - 1]); Table[ f[n], {n, 2, 53}]
CROSSREFS
Sequence in context: A024519 A160664 A345140 * A169740 A360419 A282044
KEYWORD
nonn,changed
AUTHOR
Lekraj Beedassy, Jul 22 2002
EXTENSIONS
Edited and extended by Robert G. Wilson v, Jul 23 2002
More terms from David Terr, Jan 03 2005
STATUS
approved